Asymptotic behavior of solutions of the Navier-stokes equations

1966 ◽  
Vol 22 (1) ◽  
pp. 15-21 ◽  
Author(s):  
D. E. Edmunds
Keyword(s):  
Asymptotic Behavior ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Navier Stokes Equations

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS FOR A 1D ISOTHERMAL VISCOUS GAS

2008 ◽  
Vol 18 (08) ◽  
pp. 1383-1408 ◽  
Author(s):  
YUMING QIN ◽  
YANLI ZHAO
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Stokes Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Navier Stokes Equations ◽  
Viscous Gas ◽  
Initial Boundary Value

In this paper, we prove the global existence and asymptotic behavior of solutions in Hi(i = 1, 2) to an initial boundary value problem of a 1D isentropic, isothermal and the compressible viscous gas with an non-autonomous external force in a bounded region.

scholarly journals Asymptotic Behavior of the Solutions of the Generalized Globally Modified Navier–Stokes Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yonghong Duan ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Global Attractors ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations

The paper is concerned with the existence and the asymptotic behavior of solutions to a class of generalized Navier–Stokes equations, which generalises the so-called globally modified Navier–Stokes equations. The existence and uniqueness of solutions are proved under different assumptions on the dissipation and modification factors. For the asymptotic behavior of solutions, we prove the existence of global attractors in proper spaces. The results generalize some results derived in our previous work Ann. Polon. Math. 122(2):101–128(2019).

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